2018 Key Stage 1 Mathematics Paper 2: Reasoning

What are we being asked to find?

We need to add three numbers together: 20, 2, and 2.

We can add the ones first.

\( 2 + 2 = 4 \)

Now add this to 20.

\( 20 + 4 = 24 \)

What do the parts mean?

“Four tens” means \( 40 \).

“Two ones” means \( 2 \).

We put the tens and ones together.

\( 40 + 2 = 42 \)

The digit 4 goes in the tens place, and the digit 2 goes in the ones place.

The circle is divided into 4 equal parts.

One of these 4 parts is shaded.

Since 1 out of 4 parts is shaded, the fraction is one quarter.

In numbers, we write this as \( \frac{1}{4} \).

What do we know?

The jar is full when it has 20 marbles.

It currently has 13 marbles inside.

We need to find how many more are needed to reach 20.

We can count up from 13 to 20 or subtract 13 from 20.

\( 20 – 13 = 7 \)

We need to find a number that, when multiplied by itself, equals 25.

This is like asking: “What number squared makes 25?”

Let’s check our times tables:

\( 2 \times 2 = 4 \)

\( 3 \times 3 = 9 \)

\( 4 \times 4 = 16 \)

\( 5 \times 5 = 25 \)

We need to look at the top of each tower to see which is highest.

• Tower C is clearly the highest (tallest).
• Tower D is the next tallest.
• Tower A is shorter than D.
• Tower B is the shortest of all.

Order: Tallest → Shortest

1. C (Tallest)

2. D (Given)

3. A

4. B (Shortest)

Look at the individual parts of the picture.

There is a large long shape with 4 sides and 4 right angles. This is a rectangle.

There is a round shape. This is a circle.

The rectangle is split into 4 equal boxes.

The denominator (bottom number) is 4, which matches the number of boxes.

The numerator (top number) is 3.

This tells us we need to shade 3 of the boxes.

We need to count only the black beads from left to right.

1st black bead is at the start.

2nd black bead is the 3rd bead.

3rd black bead is the 7th bead.

4th black bead is the 9th bead.

Let’s count how many bags there are.

Top row: 5 bags.

Bottom row: 5 bags.

Total bags = \( 5 + 5 = 10 \).

There are 10 balls in each bag.

We need to calculate \( 10 \times 10 \).

Counting in tens: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100.

To compare the times, we should convert them all to minutes.

We know that 1 hour = 60 minutes.

• Swimming: 45 minutes
• Art: 2 hours = \( 60 + 60 = \) 120 minutes
• Music: 75 minutes
• Drama: 1 hour = 60 minutes

Now we compare the minutes:

120 (Art) is bigger than 75, 60, and 45.

The plant grows, which means it gets bigger.

We need to add the new growth to the original height.

Original height: 11 cm

Growth: 7 cm

\( 11 + 7 = 18 \)

In the first picture, Amy makes 25.

We see 2 triangles and 5 squares.

The number 25 has 2 tens and 5 ones.

This tells us:

• 1 Triangle = 10
• 1 Square = 1

In the second picture, we have:

• 3 Triangles = 3 tens = 30
• 4 Squares = 4 ones = 4

Add them together:

\( 30 + 4 = 34 \)

Count the number of blocks for Kemi and Sam.

• Kemi has 6 blocks.
• Sam has 2 blocks.

“How many more” means we need to find the difference.

\( 6 – 2 = 4 \)

Number of tables = 6

Children per table = 5

We need to multiply the number of tables by the number of children at each table.

\( 6 \times 5 \) or \( 5 \times 6 \)

Count in 5s six times: 5, 10, 15, 20, 25, 30.

\( 6 \times 5 = 30 \)

We have a total of 20 fish.

We are sharing them equally into 5 bowls.

Sharing equally means we need to divide.

\( 20 \div 5 = ? \)

We can count in 5s until we reach 20:

5, 10, 15, 20.

That is 4 groups of 5.

A line of symmetry means if you fold the shape in half, both sides match exactly.

• Heart: Yes, down the middle.
• Shield: Yes, down the middle.
• Gingerbread Man: Yes, down the middle.
• Star: Yes, down the middle (and other ways).
• House: Yes, down the middle.

Look at the vase (the last shape).

One side curves differently from the other.

If you folded it down the middle, the sides would not match.

Ajay has 20p in total.

All his money is in 2p coins.

We need to find how many 2s fit into 20.

Count in 2s until you reach 20:

2, 4, 6, 8, 10, 12, 14, 16, 18, 20.

That is 10 fingers (or counts).

Alternatively, \( 20 \div 2 = 10 \).

The numbers 5, 8, and 40 are a family.

We know that \( 5 \times 8 = 40 \).

We need to create other correct sentences using only these three numbers.

We can swap the numbers being multiplied.

\( 8 \times 5 = 40 \)

For division, we start with the biggest number (40).

\( 40 \div 5 = 8 \)

OR

\( 40 \div 8 = 5 \)

Look at the numbers we have: 70 and 90.

Let’s count the number of gaps (jumps) between them.

There are 4 jumps from 70 to 90.

The difference is \( 90 – 70 = 20 \).

If 4 jumps = 20, then 1 jump = 5 (because \( 20 \div 4 = 5 \)).

Let’s count in 5s starting from 70:

• Start: 70
• 1st mark: 75
• 2nd mark: 80
• 3rd mark (The Box): 85
• 4th mark: 90 (This matches!)

The question tells us about planes landing every minute.

We need to find the number for 1 hour.

We know that: \( 1 \text{ hour} = 60 \text{ minutes} \).

If 1 plane lands every 1 minute, then in 60 minutes:

\( 1 \times 60 = 60 \text{ planes} \)

We need to find two numbers from the list (5, 15, 25, 35, 45, 55) that add up to 60.

• If we pick 5, we need 55. ( \( 5 + 55 = 60 \) )
• If we pick 15, we need 45. ( \( 15 + 45 = 60 \) )
• If we pick 25, we need 35. ( \( 25 + 35 = 60 \) )

The question says to use four different number cards.

This means we cannot use the same pair twice.

We can choose any two of the pairs we found.

Sam has 55p.

Ben has 10p less.

\( 55 – 10 = 45\text{p} \)

We need to select coins that add up to 45p.

Looking at the coins available:

• 20p + 20p = 40p
• Add a 5p coin = 45p

Option 1: Two 20p coins and one 5p coin.

(Another way might be 20p + 10p + 10p + 5p if available, but 20+20+5 is the simplest using the coins shown).

Sam buys 3 biscuits.

Each biscuit is 20p.

\( 20\text{p} + 20\text{p} + 20\text{p} = 60\text{p} \)

(Or \( 3 \times 20 = 60 \))

Sam buys 1 cake.

Each cake is 25p.

Now add this to the biscuit total:

\( 60\text{p} + 25\text{p} \)

\( 60 + 20 = 80 \)

\( 80 + 5 = 85 \)

Total = 85p

Change is the money you get back when you pay too much.

We need to subtract the cost from the money given.

\( 50\text{p} – 35\text{p} \)

We can count up from 35 to 50.

35 to 40 is 5.

40 to 50 is 10.

\( 10 + 5 = 15 \)

The pattern of sticks is: Long, Short, Long, Short…

The numbers are counting in 5s: 5, 10, 15, 20, 25, 30, 35, 40, 45…

The last stick shown is 45 (Long).

The next stick will be Short.

The next number after 45 (counting in 5s) is \( 45 + 5 = 50 \).

Look at the level of the grey bar on each thermometer.

• Playground: The bar stops at 15°C.
• Classroom: The bar stops at 20°C.

We need to find the difference between 20 and 15.

\( 20 – 15 = 5 \)

We have: \( \Box + \Box = 26 \)

Since the numbers in the boxes must be the same, we are adding a number to itself to get 26.

This is the same as finding half of 26.

We can partition 26 into 20 and 6.

Half of 20 is 10.

Half of 6 is 3.

\( 10 + 3 = 13 \)

Check: \( 13 + 13 = 26 \).

On this grid, 1 large square usually represents 1cm.

You need to draw a shape that is:

• 7 squares across (long)
• 3 squares down (wide)

Draw a straight line 7 squares long.

Turn the corner and draw a line 3 squares down.

Complete the rectangle.

Ben has 7 bags.

Each bag has 10 grapes.

\( 7 \times 10 = 70 \) grapes.

He gives away 25 grapes.

We need to subtract 25 from 70.

\( 70 – 25 = ? \)

Subtract 20 first: \( 70 – 20 = 50 \).

Then subtract 5: \( 50 – 5 = 45 \).

The equals sign (\(=\)) means both sides must have the same total.

Let’s calculate the left side first:

\( 13 + 6 = 19 \)

Now the right side must also equal 19.

\( 10 + \Box = 19 \)

We know that \( 19 – 10 = 9 \).

Rule 1: The difference between the numbers must be 2.

Rule 2: Both numbers must be greater than 20.

Let’s start with a number bigger than 20, e.g., 22.

We need a number that is 2 smaller than 22.

\( 22 – 20 = 2 \)

Wait! Is 20 “greater than 20”? No. So we can’t use 20.

Let’s try higher.

Start with 24.

\( 24 – 22 = 2 \)

Are both greater than 20? Yes.